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who had refused to abandon the ruins of her cottage and who
insisted on sharing her meagre supper with them.
Poincare never forgot this, nor did he ever forget the long
occupation of Nancy by the enemy. It was during the war that
he mastered German. Unable to get any French news, and eager
to learn what the Germans had to say of France and for them-
selves, Poincare taught himself the language. What he had seen
and what he learned from the official accounts of the invaders
themselves made him a flaming patriot for life but, like Her-
mite, he never confused the mathematics of his country's
enemies with their more practical activities. Cousin Raymond,
on the other hand, could never say anything about les Alle-
mands (the Germans) without an accompanying scream of hate.
In the bookkeeping of hell which balances the hate of one
patriot against that of another, Poincare* may be checked off
against Kummer, Hennite against Gauss, thus producing that
perfect zero implied in the scriptural contract 'an eye for an eye
and a tooth for a tooth*.
Following the usual French custom Poincare took the
examinations for his first degrees (bachelor of letters, and of
science) before specializing. These he passed in 1871 at the age
of seventeen - after almost failing in mathematics! He had
arrived late and flustered at the examination and had fallen
down on the extremely simple proof of the formula giving the
sum of a convergent geometrical progression. But his fame had
preceded him. *Any student other than Poincare would have
been plucked', the head examiner declared.
He next prepared for the entrance examinations to the School
of Forestry, where he astonished his companions by capturing
the first prize in mathematics without having bothered to take
any lecture notes. His classmates had previously tested him out,
believing himn to be a trifler, by delegating a fourth-year student
to quiz friyn on a mathematical difficulty which had seemed
particularly tough. Without apparent thought, Poincare gave
the solution immediately and walked off, leaving his crestfallen
baiters asking 'How does he do it?' Others were to ask the same
question all through Poincare's career. He never seemed to
think when a mathematical difficulty was submitted to him by